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Denominators of continued fraction convergents to sqrt(927).
2

%I #19 Sep 08 2022 08:44:55

%S 1,2,9,47,150,797,3338,7473,451718,910909,4095354,21387679,68258391,

%T 362679634,1518976927,3400633488,205556986207,414514605902,

%U 1863615409815,9732591654977,31061390374746,165039543528707,691219564489574,1547478672507855,93539939914960874

%N Denominators of continued fraction convergents to sqrt(927).

%H Vincenzo Librandi, <a href="/A042793/b042793.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 455056, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^14 -2*x^13 +9*x^12 -47*x^11 +150*x^10 -797*x^9 +3338*x^8 -7473*x^7 -3338*x^6 -797*x^5 -150*x^4 -47*x^3 -9*x^2 -2*x -1) / (x^16 -455056*x^8 +1). - _Colin Barker_, Dec 23 2013

%F a(n) = 455056*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Jan 29 2014

%p convert(sqrt(927), confrac, 30, cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 23 2013

%t Denominator[Convergents[Sqrt[927], 30]] (* _Wesley Ivan Hurt_, Dec 23 2013 *)

%o (Magma) I:=[1,2,9,47,150,797,3338,7473,451718,910909, 4095354,21387679,68258391,362679634,1518976927,3400633488]; [n le 16 select I[n] else 455056*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Jan 29 2014

%Y Cf. A042792, A040896.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 23 2013